JPE - Sept09 - cover2-4.pmd - Pipes & Pipelines International ...

160
J, N/mm
80
60
40
20
case (height = 3mm, length = 50mm, ligament =
3mm), the following is observed based on results in
Table 2:
• increasing the height from 3 to 6 and 9mm
leads to reductions in M of 3.8 and
J2B E 0.5%
5.5%, respectively;
• increasing the ligament from 3 to 6 and
9mm, leads to increases in M of 1.8
J2B E 0.5%
and 2.3%, respectively;
• increasing the length from 50 to 100 and
200mm leads to reductions in M of
J2B E 0.5%
1.1 and 1.8%, respectively.
• The J-based limit loads for flaws located at a given
ligament from the ID are nearly equal to those for
flaws located at the same ligament from the OD (for
example E1BH3L50L3M0 and E1BH3L50L14M0).
• M J2B E (with J e based on the elastic pipe bending
stress) is higher than M J2B EP (with J e based on the
elastic-plastic pipe-bending stress) by approximately
4%. This is not surprising since in the former case,
for a given load level, the elastic driving force (J e ) and
f(L r ) are higher, L r is lower, and M J is higher, see
Equns 2 and 7.
Comparison of flat-plate solutions
with J-based solutions
To facilitate comparison of the J-based limit loads with the
codified flat-plate solutions reviewed earlier, the M J results
The Journal of Pipeline Engineering
OD=400mm, t=20mm, e=0.0mm. Embedded flaw near ID: 2a=3.0mm, 2c=50.0mm, pi=3mm, 'E1BH3L50L3M0'
J estimate based on σ ref/σ M1 determined at 0.5% strain
J max (FEA)
J estimate based on M J2B EP 0.5% x (σ M1/σ M)
J estimate based on M J2B EP 0.5%
J estimate based on Global collapse,
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Remote strain %
Fig. 11. J results for model E1BH3L50L3M0 (from FEA and based on estimates of limit moment).
(M J2B E 0.5% and M J2B EP 0.5% ) were expressed in terms of the
non-dimensional parameter s ref /s M1 , where s M1 is the elasticplastic
pipe-bending stress, and compared with s ref /s M1
determined from the flat-plate solutions (as 1/n L ). The
results are given in Table 3. The same results are reproduced
as the ratio of s ref from the flat-plate solutions to s ref from
M J2B EP 0.5% in Table 4. The following conclusions are drawn:
Sample issue
• s ref /s M1 estimates based on flat-plate solutions and
local collapse with pin loading exceed significantly
s ref /s M1 based on M J2B E 0.5% and M J2B EP 0.5% . Therefore,
flat-plate solutions based on local collapse with pin
loading lead to conservative assessments according
to the following ranking (given in order of decreasing
conservatism):
• R6, local collapse, solution (b), pin loading
(Equn 18)
• BS 7910, local collapse, solution (a), pin
loading (Equn 11)
• R6, local collapse, solution (a), pin loading
(Equn 15)
• Table 4 shows that the BS 7910 flat-plate s ref solution
exceeds s ref based on M J2B EP 0.5% by a margin which
varies depending on flaw size and ligament. The
margin is higher for deeper and longer flaws. Except
for the shortest flaw considered (length = 25mm)
and shallow flaws located near the middle of the
thickness (height = 3mm and ligament >= 6mm) the
margin exceeds 5%. These results apply to the
stress-strain curve considered (low work hardening).